Semiconductor devices are manufactured through several processes including a process of polishing a dielectric film, e.g., SiO2, and a process of polishing a metal film, e.g., copper or tungsten. Manufacturing processes of backside illumination CMOS sensor and through-silicon via (TSV) include a process of polishing a silicon layer (silicon wafer), in addition to the polishing processes of the dielectric film and the metal film.
Polishing of a wafer is terminated when a thickness of a film (e.g., the dielectric film, the metal film, or the silicon layer), constituting a wafer surface, has reached a predetermined target value. Therefore, the thickness of the film is measured during polishing of the wafer. An optical film-thickness measuring method, disclosed in a patent documents 1, 2, is one example of a film-thickness measuring method. This method includes the steps of directing light from a film-thickness sensor to a wafer during polishing of the wafer, obtaining a spectral waveform indicating a relationship between intensity and frequency of reflected light from the wafer, obtaining a frequency spectrum by performing a Fourier transform processing on the spectral waveform, and determining a film thickness from a peak of the frequency spectrum obtained.
FIG. 12 is a graph showing an example of the spectral waveform. In FIG. 12, vertical axis represents relative reflectance indicating the intensity of the reflected light from the wafer, and horizontal axis represents frequency of the reflected light. The relative reflectance is an index value that represents the intensity of the reflected light. Specifically, the relative reflectance is a ratio of the intensity of the light to a predetermined reference intensity. By dividing the intensity of the light (i.e., the actually measured intensity) at each wavelength by a predetermined reference intensity, unwanted noises, such as a variation in the intensity inherent in an optical system or the light source of the apparatus, are removed from the actually measured intensity.
The reference intensity is an intensity that has been obtained in advance at each of the wavelengths. The relative reflectance is calculated at each of the wavelengths. Specifically, the relative reflectance is determined by dividing the intensity of the light (the actual intensity) at each wavelength by the corresponding reference intensity. The reference intensity is obtained by directly measuring the intensity of light emitted from a film-thickness sensor, or by irradiating a mirror with light from a film-thickness sensor and measuring the intensity of reflected light from the mirror. Alternatively, the reference intensity may be an intensity of the reflected light obtained when a silicon wafer (bare wafer) with no film thereon is being water-polished in the presence of water. In the actual polishing process, a dark level (which is a background intensity obtained under the condition that the light is cut off) is subtracted from the actually measured intensity to determine a corrected actually measured intensity. Further, the dark level is subtracted from the reference intensity to determine a corrected reference intensity. Then the relative reflectance is calculated by dividing the corrected actually measured intensity by the corrected reference intensity. That is, the relative reflectance R(λ) can be calculated by using
      R    ⁡          (      λ      )        =                    E        ⁡                  (          λ          )                    -              D        ⁡                  (          λ          )                                    B        ⁡                  (          λ          )                    -              D        ⁡                  (          λ          )                    where λ is wavelength, E(λ) is the intensity of the light reflected from the wafer at the wavelength λ B(λ) is the reference intensity at the wavelength λ, and D(λ) is the background intensity (i.e., dark level) at the wavelength λ obtained under the condition that the light is cut off.
FIG. 13 is a graph showing the frequency spectrum obtained by performing the Fourier transform processing on the spectral waveform shown in FIG. 12. In FIG. 13, vertical axis represents strength of a frequency component contained in the spectral waveform, and horizontal axis represents film thickness. The strength of the frequency component corresponds to an amplitude of the frequency component which is expressed as sine wave. The frequency component contained in the spectral waveform is converted into a film thickness with use of a predetermined relational expression, so that the frequency spectrum as shown in FIG. 13 is generated. This frequency spectrum represents a relationship between the film thickness and the strength of the frequency component. The above-mentioned predetermined relational expression is a linear function representing the film thickness and having the frequency component as variable. This linear function can be obtained from actual measurement results, an optical film-thickness measurement simulation, or other process.
In the graph shown in FIG. 13, the strength of the frequency component becomes maximum at a film thickness of t1. That is, this frequency spectrum indicates that the film thickness is t1. In this manner, the film thickness is determined from the peak of the frequency spectrum.